二阶离散Neumann边值问题的Ambrosetti-Prodi型结果

doi:10.6040/j.issn.1671-9352.0.2020.351

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (2): 64-74.doi: 10.6040/j.issn.1671-9352.0.2020.351

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二阶离散Neumann边值问题的Ambrosetti-Prodi型结果

杨晓梅,路艳琼,王瑞

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2021-01-21
作者简介:杨晓梅(1996— ),女,硕士研究生,研究方向为差分方程及其应用. E-mail:1269469254@qq.com
基金资助:
国家自然科学基金青年基金资助项目(11901464,11801453);西北师范大学青年教师科研能力提升计划资助项目(NWNU-LKQN2020-20)

Ambrosetti-Prodi type results of the second-order discrete Neumann boundary value problem

YANG Xiao-mei, LU Yan-qiong, WANG Rui

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2021-01-21

摘要/Abstract

摘要： 运用上下解方法和拓扑度理论,研究二阶离散Neumann边值问题{Δ²u(t-1)+g(t,u(t))=s, t∈［1,T］_Z,Δu(0)=Δu(T)=0解的个数与参数s的关系,其中s∈R, g:［1,T］_Z×R→R连续,［1,T］_Z:={1, 2, …, T},存在一个常数 s₀∈R,使得当s0时,该问题无解;s=s₀时,该问题至少有一个解;s>s₀时,该问题至少有两个解。

关键词: Neumann边值问题, Ambrosetti-Prodi问题, 上下解方法, 拓扑度理论

Abstract: By using the method of the upper and lower solutions and topological degree, this paper obtains the relationship between s and the number of solutions for the second-order discrete Neumann boundary value problem{ Δ²u(t-1)+g(t,u(t))=s, t∈［1,T］_Z,Δu(0)=Δu(T)=0,where s∈R is a real parameter, g:［1,T］_Z×R→R is continuous,［1,T］_Z:={1, 2, …, T}, there exists s₀∈R such that the problem has no solution if s0, at least one solution if s=s0 and at least two solutions if s>s0。

Key words: Neumann boundary value problem, Ambrosetti-Prodi problem, lower and upper solutions method, topological degree theory

中图分类号:

O175.7

杨晓梅,路艳琼,王瑞. 二阶离散Neumann边值问题的Ambrosetti-Prodi型结果[J]. 《山东大学学报(理学版)》, 2021, 56(2): 64-74.

YANG Xiao-mei, LU Yan-qiong, WANG Rui. Ambrosetti-Prodi type results of the second-order discrete Neumann boundary value problem[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 64-74.

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二阶离散Neumann边值问题的Ambrosetti-Prodi型结果

Ambrosetti-Prodi type results of the second-order discrete Neumann boundary value problem

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